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epnp.cpp
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9 
10 #include "vision-precomp.h" // Precompiled headers
11 #include <mrpt/config.h>
12 #include <iostream>
13 
14 // Opencv 2.3 had a broken <opencv/eigen.h> in Ubuntu 14.04 Trusty => Disable PNP classes
15 #include <mrpt/config.h>
16 #if MRPT_HAS_OPENCV && MRPT_OPENCV_VERSION_NUM<0x240
17 # undef MRPT_HAS_OPENCV
18 # define MRPT_HAS_OPENCV 0
19 #endif
20 
21 #if MRPT_HAS_OPENCV
22  #include <mrpt/otherlibs/do_opencv_includes.h>
23  using namespace cv;
24 
25  #include "epnp.h"
26 
27  mrpt::vision::pnp::epnp::epnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints)
28  {
29  if (cameraMatrix.depth() == CV_32F)
30  init_camera_parameters<float>(cameraMatrix);
31  else
32  init_camera_parameters<double>(cameraMatrix);
33 
34  number_of_correspondences = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
35 
36  pws.resize(3 * number_of_correspondences);
37  us.resize(2 * number_of_correspondences);
38 
39  if (opoints.depth() == ipoints.depth())
40  {
41  if (opoints.depth() == CV_32F)
42  init_points<cv::Point3f,cv::Point2f>(opoints, ipoints);
43  else
44  init_points<cv::Point3d,cv::Point2d>(opoints, ipoints);
45  }
46  else if (opoints.depth() == CV_32F)
47  init_points<cv::Point3f,cv::Point2d>(opoints, ipoints);
48  else
49  init_points<cv::Point3d,cv::Point2f>(opoints, ipoints);
50 
51  alphas.resize(4 * number_of_correspondences);
52  pcs.resize(3 * number_of_correspondences);
53 
54  max_nr = 0;
55  A1 = NULL;
56  A2 = NULL;
57  }
58 
60  {
61  if (A1)
62  delete[] A1;
63  if (A2)
64  delete[] A2;
65  }
66 
68  {
69  // Take C0 as the reference points centroid:
70  cws[0][0] = cws[0][1] = cws[0][2] = 0;
71  for(int i = 0; i < number_of_correspondences; i++)
72  for(int j = 0; j < 3; j++)
73  cws[0][j] += pws[3 * i + j];
74 
75  for(int j = 0; j < 3; j++)
76  cws[0][j] /= number_of_correspondences;
77 
78 
79  // Take C1, C2, and C3 from PCA on the reference points:
80  CvMat * PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F);
81 
82  double pw0tpw0[3 * 3], dc[3], uct[3 * 3];
83  CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0);
84  CvMat DC = cvMat(3, 1, CV_64F, dc);
85  CvMat UCt = cvMat(3, 3, CV_64F, uct);
86 
87  for(int i = 0; i < number_of_correspondences; i++)
88  for(int j = 0; j < 3; j++)
89  PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j];
90 
91  cvMulTransposed(PW0, &PW0tPW0, 1);
92  cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
93 
94  cvReleaseMat(&PW0);
95 
96  for(int i = 1; i < 4; i++) {
97  double k = sqrt(dc[i - 1] / number_of_correspondences);
98  for(int j = 0; j < 3; j++)
99  cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j];
100  }
101  }
102 
104  {
105  double cc[3 * 3], cc_inv[3 * 3];
106  CvMat CC = cvMat(3, 3, CV_64F, cc);
107  CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv);
108 
109  for(int i = 0; i < 3; i++)
110  for(int j = 1; j < 4; j++)
111  cc[3 * i + j - 1] = cws[j][i] - cws[0][i];
112 
113  cvInvert(&CC, &CC_inv, CV_SVD);
114  double * ci = cc_inv;
115  for(int i = 0; i < number_of_correspondences; i++) {
116  double * pi = &pws[0] + 3 * i;
117  double * a = &alphas[0] + 4 * i;
118 
119  for(int j = 0; j < 3; j++)
120  a[1 + j] =
121  ci[3 * j ] * (pi[0] - cws[0][0]) +
122  ci[3 * j + 1] * (pi[1] - cws[0][1]) +
123  ci[3 * j + 2] * (pi[2] - cws[0][2]);
124  a[0] = 1.0f - a[1] - a[2] - a[3];
125  }
126  }
127 
128  void mrpt::vision::pnp::epnp::fill_M(CvMat * M,
129  const int row, const double * as, const double u, const double v)
130  {
131  double * M1 = M->data.db + row * 12;
132  double * M2 = M1 + 12;
133 
134  for(int i = 0; i < 4; i++) {
135  M1[3 * i ] = as[i] * fu;
136  M1[3 * i + 1] = 0.0;
137  M1[3 * i + 2] = as[i] * (uc - u);
138 
139  M2[3 * i ] = 0.0;
140  M2[3 * i + 1] = as[i] * fv;
141  M2[3 * i + 2] = as[i] * (vc - v);
142  }
143  }
144 
145  void mrpt::vision::pnp::epnp::compute_ccs(const double * betas, const double * ut)
146  {
147  for(int i = 0; i < 4; i++)
148  ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
149 
150  for(int i = 0; i < 4; i++) {
151  const double * v = ut + 12 * (11 - i);
152  for(int j = 0; j < 4; j++)
153  for(int k = 0; k < 3; k++)
154  ccs[j][k] += betas[i] * v[3 * j + k];
155  }
156  }
157 
159  {
160  for(int i = 0; i < number_of_correspondences; i++) {
161  double * a = &alphas[0] + 4 * i;
162  double * pc = &pcs[0] + 3 * i;
163 
164  for(int j = 0; j < 3; j++)
165  pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j];
166  }
167  }
168 
169  void mrpt::vision::pnp::epnp::compute_pose(cv::Mat& R, cv::Mat& t)
170  {
171  choose_control_points();
172  compute_barycentric_coordinates();
173 
174  CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
175 
176  for(int i = 0; i < number_of_correspondences; i++)
177  fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
178 
179  double mtm[12 * 12], d[12], ut[12 * 12];
180  CvMat MtM = cvMat(12, 12, CV_64F, mtm);
181  CvMat D = cvMat(12, 1, CV_64F, d);
182  CvMat Ut = cvMat(12, 12, CV_64F, ut);
183 
184  cvMulTransposed(M, &MtM, 1);
185  cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
186  cvReleaseMat(&M);
187 
188  double l_6x10[6 * 10], rho[6];
189  CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10);
190  CvMat Rho = cvMat(6, 1, CV_64F, rho);
191 
192  compute_L_6x10(ut, l_6x10);
193  compute_rho(rho);
194 
195  double Betas[4][4], rep_errors[4];
196  double Rs[4][3][3], ts[4][3];
197 
198  find_betas_approx_1(&L_6x10, &Rho, Betas[1]);
199  gauss_newton(&L_6x10, &Rho, Betas[1]);
200  rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
201 
202  find_betas_approx_2(&L_6x10, &Rho, Betas[2]);
203  gauss_newton(&L_6x10, &Rho, Betas[2]);
204  rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
205 
206  find_betas_approx_3(&L_6x10, &Rho, Betas[3]);
207  gauss_newton(&L_6x10, &Rho, Betas[3]);
208  rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]);
209 
210  int N = 1;
211  if (rep_errors[2] < rep_errors[1]) N = 2;
212  if (rep_errors[3] < rep_errors[N]) N = 3;
213 
214  cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
215  cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
216  }
217 
218  void mrpt::vision::pnp::epnp::copy_R_and_t(const double R_src[3][3], const double t_src[3],
219  double R_dst[3][3], double t_dst[3])
220  {
221  for(int i = 0; i < 3; i++) {
222  for(int j = 0; j < 3; j++)
223  R_dst[i][j] = R_src[i][j];
224  t_dst[i] = t_src[i];
225  }
226  }
227 
228  double mrpt::vision::pnp::epnp::dist2(const double * p1, const double * p2)
229  {
230  return
231  (p1[0] - p2[0]) * (p1[0] - p2[0]) +
232  (p1[1] - p2[1]) * (p1[1] - p2[1]) +
233  (p1[2] - p2[2]) * (p1[2] - p2[2]);
234  }
235 
236  double mrpt::vision::pnp::epnp::dot(const double * v1, const double * v2)
237  {
238  return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
239  }
240 
241  void mrpt::vision::pnp::epnp::estimate_R_and_t(double R[3][3], double t[3])
242  {
243  double pc0[3], pw0[3];
244 
245  pc0[0] = pc0[1] = pc0[2] = 0.0;
246  pw0[0] = pw0[1] = pw0[2] = 0.0;
247 
248  for(int i = 0; i < number_of_correspondences; i++) {
249  const double * pc = &pcs[3 * i];
250  const double * pw = &pws[3 * i];
251 
252  for(int j = 0; j < 3; j++) {
253  pc0[j] += pc[j];
254  pw0[j] += pw[j];
255  }
256  }
257  for(int j = 0; j < 3; j++) {
258  pc0[j] /= number_of_correspondences;
259  pw0[j] /= number_of_correspondences;
260  }
261 
262  double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3];
263  CvMat ABt = cvMat(3, 3, CV_64F, abt);
264  CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d);
265  CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u);
266  CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v);
267 
268  cvSetZero(&ABt);
269  for(int i = 0; i < number_of_correspondences; i++) {
270  double * pc = &pcs[3 * i];
271  double * pw = &pws[3 * i];
272 
273  for(int j = 0; j < 3; j++) {
274  abt[3 * j ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
275  abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
276  abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
277  }
278  }
279 
280  cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A);
281 
282  for(int i = 0; i < 3; i++)
283  for(int j = 0; j < 3; j++)
284  R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
285 
286  const double det =
287  R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] -
288  R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
289 
290  if (det < 0) {
291  R[2][0] = -R[2][0];
292  R[2][1] = -R[2][1];
293  R[2][2] = -R[2][2];
294  }
295 
296  t[0] = pc0[0] - dot(R[0], pw0);
297  t[1] = pc0[1] - dot(R[1], pw0);
298  t[2] = pc0[2] - dot(R[2], pw0);
299  }
300 
302  {
303  if (pcs[2] < 0.0) {
304  for(int i = 0; i < 4; i++)
305  for(int j = 0; j < 3; j++)
306  ccs[i][j] = -ccs[i][j];
307 
308  for(int i = 0; i < number_of_correspondences; i++) {
309  pcs[3 * i ] = -pcs[3 * i];
310  pcs[3 * i + 1] = -pcs[3 * i + 1];
311  pcs[3 * i + 2] = -pcs[3 * i + 2];
312  }
313  }
314  }
315 
316  double mrpt::vision::pnp::epnp::compute_R_and_t(const double * ut, const double * betas,
317  double R[3][3], double t[3])
318  {
319  compute_ccs(betas, ut);
320  compute_pcs();
321 
322  solve_for_sign();
323 
324  estimate_R_and_t(R, t);
325 
326  return reprojection_error(R, t);
327  }
328 
329  double mrpt::vision::pnp::epnp::reprojection_error(const double R[3][3], const double t[3])
330  {
331  double sum2 = 0.0;
332 
333  for(int i = 0; i < number_of_correspondences; i++) {
334  double * pw = &pws[3 * i];
335  double Xc = dot(R[0], pw) + t[0];
336  double Yc = dot(R[1], pw) + t[1];
337  double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
338  double ue = uc + fu * Xc * inv_Zc;
339  double ve = vc + fv * Yc * inv_Zc;
340  double u = us[2 * i], v = us[2 * i + 1];
341 
342  sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) );
343  }
344 
345  return sum2 / number_of_correspondences;
346  }
347 
348  // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
349  // betas_approx_1 = [B11 B12 B13 B14]
350 
351  void mrpt::vision::pnp::epnp::find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho,
352  double * betas)
353  {
354  double l_6x4[6 * 4], b4[4];
355  CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4);
356  CvMat B4 = cvMat(4, 1, CV_64F, b4);
357 
358  for(int i = 0; i < 6; i++) {
359  cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0));
360  cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1));
361  cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3));
362  cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6));
363  }
364 
365  cvSolve(&L_6x4, Rho, &B4, CV_SVD);
366 
367  if (b4[0] < 0) {
368  betas[0] = sqrt(-b4[0]);
369  betas[1] = -b4[1] / betas[0];
370  betas[2] = -b4[2] / betas[0];
371  betas[3] = -b4[3] / betas[0];
372  } else {
373  betas[0] = sqrt(b4[0]);
374  betas[1] = b4[1] / betas[0];
375  betas[2] = b4[2] / betas[0];
376  betas[3] = b4[3] / betas[0];
377  }
378  }
379 
380  // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
381  // betas_approx_2 = [B11 B12 B22 ]
382 
383  void mrpt::vision::pnp::epnp::find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho,
384  double * betas)
385  {
386  double l_6x3[6 * 3], b3[3];
387  CvMat L_6x3 = cvMat(6, 3, CV_64F, l_6x3);
388  CvMat B3 = cvMat(3, 1, CV_64F, b3);
389 
390  for(int i = 0; i < 6; i++) {
391  cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0));
392  cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1));
393  cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2));
394  }
395 
396  cvSolve(&L_6x3, Rho, &B3, CV_SVD);
397 
398  if (b3[0] < 0) {
399  betas[0] = sqrt(-b3[0]);
400  betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0;
401  } else {
402  betas[0] = sqrt(b3[0]);
403  betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0;
404  }
405 
406  if (b3[1] < 0) betas[0] = -betas[0];
407 
408  betas[2] = 0.0;
409  betas[3] = 0.0;
410  }
411 
412  // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
413  // betas_approx_3 = [B11 B12 B22 B13 B23 ]
414 
415  void mrpt::vision::pnp::epnp::find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho,
416  double * betas)
417  {
418  double l_6x5[6 * 5], b5[5];
419  CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5);
420  CvMat B5 = cvMat(5, 1, CV_64F, b5);
421 
422  for(int i = 0; i < 6; i++) {
423  cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0));
424  cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1));
425  cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2));
426  cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3));
427  cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4));
428  }
429 
430  cvSolve(&L_6x5, Rho, &B5, CV_SVD);
431 
432  if (b5[0] < 0) {
433  betas[0] = sqrt(-b5[0]);
434  betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0;
435  } else {
436  betas[0] = sqrt(b5[0]);
437  betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0;
438  }
439  if (b5[1] < 0) betas[0] = -betas[0];
440  betas[2] = b5[3] / betas[0];
441  betas[3] = 0.0;
442  }
443 
444  void mrpt::vision::pnp::epnp::compute_L_6x10(const double * ut, double * l_6x10)
445  {
446  const double * v[4];
447 
448  v[0] = ut + 12 * 11;
449  v[1] = ut + 12 * 10;
450  v[2] = ut + 12 * 9;
451  v[3] = ut + 12 * 8;
452 
453  double dv[4][6][3];
454 
455  for(int i = 0; i < 4; i++) {
456  int a = 0, b = 1;
457  for(int j = 0; j < 6; j++) {
458  dv[i][j][0] = v[i][3 * a ] - v[i][3 * b];
459  dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
460  dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
461 
462  b++;
463  if (b > 3) {
464  a++;
465  b = a + 1;
466  }
467  }
468  }
469 
470  for(int i = 0; i < 6; i++) {
471  double * row = l_6x10 + 10 * i;
472 
473  row[0] = dot(dv[0][i], dv[0][i]);
474  row[1] = 2.0f * dot(dv[0][i], dv[1][i]);
475  row[2] = dot(dv[1][i], dv[1][i]);
476  row[3] = 2.0f * dot(dv[0][i], dv[2][i]);
477  row[4] = 2.0f * dot(dv[1][i], dv[2][i]);
478  row[5] = dot(dv[2][i], dv[2][i]);
479  row[6] = 2.0f * dot(dv[0][i], dv[3][i]);
480  row[7] = 2.0f * dot(dv[1][i], dv[3][i]);
481  row[8] = 2.0f * dot(dv[2][i], dv[3][i]);
482  row[9] = dot(dv[3][i], dv[3][i]);
483  }
484  }
485 
486  void mrpt::vision::pnp::epnp::compute_rho(double * rho)
487  {
488  rho[0] = dist2(cws[0], cws[1]);
489  rho[1] = dist2(cws[0], cws[2]);
490  rho[2] = dist2(cws[0], cws[3]);
491  rho[3] = dist2(cws[1], cws[2]);
492  rho[4] = dist2(cws[1], cws[3]);
493  rho[5] = dist2(cws[2], cws[3]);
494  }
495 
496  void mrpt::vision::pnp::epnp::compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho,
497  const double betas[4], CvMat * A, CvMat * b)
498  {
499  for(int i = 0; i < 6; i++) {
500  const double * rowL = l_6x10 + i * 10;
501  double * rowA = A->data.db + i * 4;
502 
503  rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[3] * betas[2] + rowL[6] * betas[3];
504  rowA[1] = rowL[1] * betas[0] + 2 * rowL[2] * betas[1] + rowL[4] * betas[2] + rowL[7] * betas[3];
505  rowA[2] = rowL[3] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + rowL[8] * betas[3];
506  rowA[3] = rowL[6] * betas[0] + rowL[7] * betas[1] + rowL[8] * betas[2] + 2 * rowL[9] * betas[3];
507 
508  cvmSet(b, i, 0, rho[i] -
509  (
510  rowL[0] * betas[0] * betas[0] +
511  rowL[1] * betas[0] * betas[1] +
512  rowL[2] * betas[1] * betas[1] +
513  rowL[3] * betas[0] * betas[2] +
514  rowL[4] * betas[1] * betas[2] +
515  rowL[5] * betas[2] * betas[2] +
516  rowL[6] * betas[0] * betas[3] +
517  rowL[7] * betas[1] * betas[3] +
518  rowL[8] * betas[2] * betas[3] +
519  rowL[9] * betas[3] * betas[3]
520  ));
521  }
522  }
523 
524  void mrpt::vision::pnp::epnp::gauss_newton(const CvMat * L_6x10, const CvMat * Rho, double betas[4])
525  {
526  const int iterations_number = 5;
527 
528  double a[6*4], b[6], x[4];
529  CvMat A = cvMat(6, 4, CV_64F, a);
530  CvMat B = cvMat(6, 1, CV_64F, b);
531  CvMat X = cvMat(4, 1, CV_64F, x);
532 
533  for(int k = 0; k < iterations_number; k++)
534  {
535  compute_A_and_b_gauss_newton(L_6x10->data.db, Rho->data.db,
536  betas, &A, &B);
537  qr_solve(&A, &B, &X);
538  for(int i = 0; i < 4; i++)
539  betas[i] += x[i];
540  }
541  }
542 
543  void mrpt::vision::pnp::epnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
544  {
545  const int nr = A->rows;
546  const int nc = A->cols;
547 
548  if (max_nr != 0 && max_nr < nr)
549  {
550  delete [] A1;
551  delete [] A2;
552  }
553  if (max_nr < nr)
554  {
555  max_nr = nr;
556  A1 = new double[nr];
557  A2 = new double[nr];
558  }
559 
560  double * pA = A->data.db, * ppAkk = pA;
561  for(int k = 0; k < nc; k++)
562  {
563  double * ppAik1 = ppAkk, eta = fabs(*ppAik1);
564  for(int i = k + 1; i < nr; i++)
565  {
566  double elt = fabs(*ppAik1);
567  if (eta < elt) eta = elt;
568  ppAik1 += nc;
569  }
570  if (eta == 0)
571  {
572  A1[k] = A2[k] = 0.0;
573  //cerr << "God damnit, A is singular, this shouldn't happen." << endl;
574  return;
575  }
576  else
577  {
578  double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
579  for(int i = k; i < nr; i++)
580  {
581  *ppAik2 *= inv_eta;
582  sum2 += *ppAik2 * *ppAik2;
583  ppAik2 += nc;
584  }
585  double sigma = sqrt(sum2);
586  if (*ppAkk < 0)
587  sigma = -sigma;
588  *ppAkk += sigma;
589  A1[k] = sigma * *ppAkk;
590  A2[k] = -eta * sigma;
591  for(int j = k + 1; j < nc; j++)
592  {
593  double * ppAik = ppAkk, sum = 0;
594  for(int i = k; i < nr; i++)
595  {
596  sum += *ppAik * ppAik[j - k];
597  ppAik += nc;
598  }
599  double tau = sum / A1[k];
600  ppAik = ppAkk;
601  for(int i = k; i < nr; i++)
602  {
603  ppAik[j - k] -= tau * *ppAik;
604  ppAik += nc;
605  }
606  }
607  }
608  ppAkk += nc + 1;
609  }
610 
611  // b <- Qt b
612  double * ppAjj = pA, * pb = b->data.db;
613  for(int j = 0; j < nc; j++)
614  {
615  double * ppAij = ppAjj, tau = 0;
616  for(int i = j; i < nr; i++)
617  {
618  tau += *ppAij * pb[i];
619  ppAij += nc;
620  }
621  tau /= A1[j];
622  ppAij = ppAjj;
623  for(int i = j; i < nr; i++)
624  {
625  pb[i] -= tau * *ppAij;
626  ppAij += nc;
627  }
628  ppAjj += nc + 1;
629  }
630 
631  // X = R-1 b
632  double * pX = X->data.db;
633  pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
634  for(int i = nc - 2; i >= 0; i--)
635  {
636  double * ppAij = pA + i * nc + (i + 1), sum = 0;
637 
638  for(int j = i + 1; j < nc; j++)
639  {
640  sum += *ppAij * pX[j];
641  ppAij++;
642  }
643  pX[i] = (pb[i] - sum) / A2[i];
644  }
645  }
646 #endif
GLboolean GLboolean GLboolean GLboolean a
Definition: glew.h:5406
void compute_A_and_b_gauss_newton(const double *l_6x10, const double *rho, const double cb[4], CvMat *A, CvMat *b)
Internal function.
const GLdouble * v
Definition: glew.h:1296
void compute_barycentric_coordinates(void)
Convert from object space to relative object space (Barycentric coordinates)
void choose_control_points(void)
Function to select 4 control points from n points.
GLenum GLenum GLvoid * row
Definition: glew.h:2903
void find_betas_approx_3(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.
void compute_pose(cv::Mat &R, cv::Mat &t)
OpenCV wrapper to compute pose.
GLfloat GLfloat v1
Definition: glew.h:1759
void compute_rho(double *rho)
Get distances between all object points taken 2 at a time(nC2)
~epnp()
Destructor for EPnP class.
GLdouble GLdouble t
Definition: glew.h:1303
double reprojection_error(const double R[3][3], const double t[3])
Function to compute reprojection error.
double dist2(const double *p1, const double *p2)
Squared distance between two vectors.
GLfloat GLfloat GLfloat v2
Definition: glew.h:1763
void gauss_newton(const CvMat *L_6x10, const CvMat *Rho, double current_betas[4])
Gauss Newton iterative algorithm.
void copy_R_and_t(const double R_dst[3][3], const double t_dst[3], double R_src[3][3], double t_src[3])
Copy function of output result.
void solve_for_sign(void)
Internal function.
void fill_M(CvMat *M, const int row, const double *alphas, const double u, const double v)
Generate the Matrix M.
double dot(const double *v1, const double *v2)
Dot product of two OpenCV vectors.
CONTAINER::Scalar sum(const CONTAINER &v)
Computes the sum of all the elements.
Efficient PnP - Eigen Wrapper for OpenCV calib3d implementation.
GLint GLint GLint GLint GLint x
Definition: glew.h:1166
void qr_solve(CvMat *A, CvMat *b, CvMat *X)
QR optimization algorithm.
double A1
UTC constant and 1st order terms.
void estimate_R_and_t(double R[3][3], double t[3])
Helper function to compute_R_and_t()
const float R
void find_betas_approx_2(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.
double compute_R_and_t(const double *ut, const double *betas, double R[3][3], double t[3])
Function to compute pose.
void compute_ccs(const double *betas, const double *ut)
Internal function.
void compute_pcs(void)
Internal function.
GLdouble GLdouble GLdouble b
Definition: glew.h:5092
EIGEN_STRONG_INLINE Scalar det() const
epnp(const cv::Mat &cameraMatrix, const cv::Mat &opoints, const cv::Mat &ipoints)
Constructor for EPnP class.
void compute_L_6x10(const double *ut, double *l_6x10)
Internal function.
GLdouble GLdouble GLdouble GLdouble GLdouble GLdouble f
Definition: glew.h:5092
void find_betas_approx_1(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.



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